Error bounds for asymptotic expansions of the ratio of two gamma functions
SIAM Journal on Mathematical Analysis
Two new asymptotic expansions of the ratio of two gamma functions
Journal of Computational and Applied Mathematics
The asymptotic series of the generalized Stirling formula
Computers & Mathematics with Applications
New approximation formulas for evaluating the ratio of gamma functions
Mathematical and Computer Modelling: An International Journal
| Hi-index | 7.29 |
The main subject of this paper is the analysis of asymptotic expansions of Wallis quotient function @C(x+t)@C(x+s) and Wallis power function [@C(x+t)@C(x+s)]^1^/^(^t^-^s^), when x tends to infinity. Coefficients of these expansions are polynomials derived from Bernoulli polynomials. The key to our approach is the introduction of two intrinsic variables @a=12(t+s-1) and @b=14(1+t-s)(1-t+s) which are naturally connected with Bernoulli polynomials and Wallis functions. Asymptotic expansion of Wallis functions in terms of variables t and s and also @a and @b is given. Application of the new method leads to the improvement of many known approximation formulas of the Stirling's type.